A physical quantity $P$ is related to four observables $a, b, c$ and $d$ as $P = \frac{a^3 b^2}{\sqrt{c} d}$. The percentage errors of measurement in $a, b, c$ and $d$ are $1\%, 3\%, 4\%$ and $2\%$ respectively. Calculate the maximum percentage error in the quantity $P$.

The density of a solid cube is determined by measuring its mass and the length of its side. If the maximum error in the measurement of mass is $3\%$ and the maximum error in the measurement of length is $2\%$, what is the maximum percentage error in the calculated density?

In a simple pendulum experiment to determine the acceleration due to gravity $g$, the length $L$ of the pendulum is measured as $100$ cm with a meter scale of least count $1$ mm. The time for $100$ oscillations is $200$ s measured with a stopwatch of least count $1$ s. What is the maximum percentage error in the value of $g$?

The number of significant figures in the measured values $0.007\text{ m}^2$, $2.64 \times 10^{24}\text{ kg}$, and $0.2370\text{ g cm}^{-3}$ are respectively:

Following the rules of rounding off, round $2.745$ and $2.735$ to three significant figures.